It doesn’t exist in such a high-level form yet, but essentially any app can connect to the launcher and ask permissions to read and write basic files into your safe-network protected area. Those are generally “sandboxed” per app (ID) and thus can have their own way of structuring the data – which most “web”-APIs are ultimately about: authenticating and fetching and storing data.
So, yes, you can build apps that act in your personal space – see my Ghost in the Safe project as an example.